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This paper considers the matrix completion problem. We show that it is not necessary to assume joint incoherence, which is a standard but unintuitive and restrictive condition that is imposed by previous studies. This leads to a sample…
Inspired by real-world applications such as the assignment of pupils to schools or the allocation of social housing, the one-sided matching problem studies how a set of agents can be assigned to a set of objects when the agents have…
This paper proposes a new deterministic sampling strategy for constructing polynomial chaos approximations for expensive physics simulation models. The proposed approach, effectively subsampled quadratures involves sparsely subsampling an…
In the bottleneck multiple knapsack problem, we are given a set of items and a set of knapsacks, where each item has a profit and a weight, and each knapsack has a capacity. Our goal is to assign items to knapsacks so as to maximize the…
Capacity sharing networks are typical heterogeneous communication networks widely applied in information and communications technology (ICT) field. In such networks, resources like bandwidth, spectrum, computation and storage are shared…
Motivated by adjacency in perfect matching polytopes, we study the shortest reconfiguration problem of perfect matchings via alternating cycles. Namely, we want to find a shortest sequence of perfect matchings which transforms one given…
Co-clustering, that is, partitioning a numerical matrix into homogeneous submatrices, has many applications ranging from bioinformatics to election analysis. Many interesting variants of co-clustering are NP-hard. We focus on the basic…
The row (column) completion problem of polynomial matrices of given degree with prescribed eigenstructure has been studied in \cite{AmBaMaRo23}, where several results of prescription of some of the four types of invariants that form the…
We consider the related tasks of matrix completion and matrix approximation from missing data and propose adaptive sampling procedures for both problems. We show that adaptive sampling allows one to eliminate standard incoherence…
Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion…
In contrast to Part I of this treatise [1] that focuses on the optimization problems associated with single matrix variables, in this paper, we investigate the application of the matrix-monotonic optimization framework in the optimization…
A matching is said to be disconnected if the saturated vertices induce a disconnected subgraph and induced if the saturated vertices induce a 1-regular graph. The disconnected and induced matching numbers are defined as the maximum…
This paper examines the problem of state estimation in power distribution systems under low-observability conditions. The recently proposed constrained matrix completion method which combines the standard matrix completion method and power…
Given a real matrix A with n columns, the problem is to approximate the Gram product AA^T by c << n weighted outer products of columns of A. Necessary and sufficient conditions for the exact computation of AA^T (in exact arithmetic) from c…
The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…
We study a problem related to submodular function optimization and the exact matching problem for which we show a rather peculiar status: its natural LP-relaxation can have fractional optimal vertices, but there is always also an optimal…
This paper addresses the task allocation problem for multi-robot systems. The main issue with the task allocation problem is inherent complexity that makes finding an optimal solution within a reasonable time almost impossible. To hand the…
The paper considers the problem of finding a submatrix $X_{\mathcal{S}} \in \mathbb{R}^{m \times k}$ in a matrix $X \in \mathbb{R}^{m \times n}$, such that the spectral or Frobenius norm of $X_{\mathcal{S}}^{\dag} X$ is limited, which…
We consider the symmetric Toeplitz matrix completion problem, whose matrix under consideration possesses specific row and column structures. This problem, which has wide application in diverse areas, is well-known to be computationally…
The Stable Roommates problem involves matching a set of agents into pairs based on the agents' strict ordinal preference lists. The matching must be stable, meaning that no two agents strictly prefer each other to their assigned partners. A…